Question

Bethany needs to borrow $8,000. She can borrow money at 6.9% simple interest for 3 yr or she can borrow at 6.5% with interest compounded continuously for 3 yr. Which option results in less total interest

Answer 1

The loan options which would result in less total interest is borrowing money at 6.9% simple interest.

Given the following data:

• Principal, P = $8,000.

• Interest rate, R = 6.9%

• Time, T = 3 years

• Interest rate 2 = 6.5%

To determine which of the loan options would result in less total interest:

For simple interest:

Mathematically, simple interest is given by the formula:

$S.I = \frac{PRT}{100}\\\\S.I = \frac{8000 \times 6.9 \times 3}{100}\\\\S.I = 80 \times 6.9 \times 3$

S.I = $1,656.

For compound interest:

Mathematically, an interest that is compounded continuously given by the formula:

$A = Pe^{rt}\\\\A = 8000 \times e^{0.065 \times 3}\\\\A = 8000 \times e^{0.195}\\\\A = 8000 \times 1.2153$

A = $9,722.49

$Interest = A -P\\\\Interest = 9722.49-8000$

Interest = $1,722.49

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